John Wallbaum

Research Interests

My research uses computability theory to study algebraic structures such as groups, orderings, and equivalence structures. I consider questions about when a structure can be presented in an computable way and about the complexity of different algorithms in the structure. In one project, our research group was able to determine how hard it is to compute a basis of a computable free group. We also calculated the most efficient way to determine if a computable group is a free group or not. In another project, I studied limitwise monotonic functions, which tell us when certain abelian p-groups and equivalence structures can be presented computably.